Many subsurface operations require a directional sensor system to measure borehole orientation or orientation of an instrument within the borehole. A directional sensor system typically comprises at least two sets of three directional sensor elements configured so that the axes of the sensor elements are orthogonal. Responses of the directional sensor elements are combined to obtain a measure of orientation of the directional sensor system in three dimensional space.
Several types of directional sensor elements are used in directional sensor systems. These types of sensor elements include magnetometers, accelerometers, and gyroscopes. The response of a directional sensor element typically includes bias, scale factor and mechanical misalignment components. Bias, scale factors and mechanical misalignment components are typically different for each of the at least three directional sensor elements. When responses of the sensor elements are combined, bias. scale factor and mechanical misalignment can be a source of error in the orientation determination. Borehole directional sensor systems are typically calibrated at the surface of the earth. Calibration includes determinations of bias and scale factor for each directional sensor element. These determinations are subsequently used to correct the individual sensor responses prior to combining to determine orientation.
Bias and scale factor of the sensor elements can change as a function of time in typically harsh borehole environment. Temperature also has a strong influence on bias and scale, especially at the higher operating temperatures of 185 to 200 degrees centigrade (° C.). It is not unusual to see hysterisis effects in sensors for which the calibration will vary when traversing the same temperature point from different directions. Furthermore, the magnitude of bias and scale factor change can be different for multiple directional sensor elements. These changes in bias and scale factor, which occur after system calibration at the surface of the earth, can result in erroneous borehole orientation determinations.